Insegnamento a.a. 2020-2021

30546 - PROBABILITY

Department of Decision Sciences

Course taught in English
Go to class group/s: 27
BAI (8 credits - II sem. - OB  |  MAT/06)
Course Director:
SANDRA FORTINI

Classes: 27 (II sem.)
Instructors:
Class 27: SANDRA FORTINI


Suggested background knowledge

Set theory. Sequences and series. Continuous and differentiable functions. Integrals. Complex numbers.

Mission & Content Summary

MISSION

Probability is the language of uncertainty. It is essential to express inherent stochasticity of the world, to describe information and lack of knowledge and to make predictions. For this reason it is the bedrock of machine learning and artificial intelligence. You cannot develop a deep understanding and application of artificial intelligence without it. The course will provide a rigorous introduction to probability. Students will gain a solid grounding on the its foundations, will learn how to deal with randomness with the correct mathematical tools and how to solve problems.

CONTENT SUMMARY

 

• Combinatorics

• Probability spaces

• Random variables and random vectors
• Expectation and integral transforms
• Simulation of random variables
• The simple random walk
• Modes of convergence for sequences of random variables
• Conditional expectation and prediction


Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • recognize appropriate models to describe a random environment;
  • identify the correct methodology for solving problems under uncertainty;
  • discuss the role of the assumptions in a probabilistic model
  • understand the mathematical proofs and dicuss the role of the hypotheses.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • translate a problem into the language of probability;
  • apply the probabilistic techniques to solve problems involving uncertainty;
  • interpret the solutions derived from implementing the chosen model;
  • develop autonomously simple mathematical proofs.

Teaching methods

  • Face-to-face lectures
  • Exercises (exercises, database, software etc.)
  • Individual assignments

DETAILS

Exercises will be proposed to students and their solution will be discussed in class. 

Individual assignment will be proposed by Blackboard tools for training and self assessment.


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
 x x x

ATTENDING AND NOT ATTENDING STUDENTS

Assessment, both for attending and non-attending students, is based on continuous assessment (20%) and partial exams or general exam (80%). 

 

Continuous assessments are made of multiple choice and numerical questions. The aim is verifying:

  • the ability to recognize appropriate models for a random environment
  • the ability to apply the correct techniques to solve problems.

 

Partial and general exams are made of theoretical and numerical questions. The aim is verifying:

  • the ability to develop autonomously simple mathematical proofs and discuss the role of the assumptions
  • the abillity to solve problems and interpret the solutions.

 


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Grimmett, G.R. & Stirzaker, D.R. (2001). Probability and Random Processes. Oxford University Press.

Last change 16/06/2020 16:12